Optical Flow (OF) generally refers to the apparent motion of brightness patterns in a sequence of images. OF techniques may be employed to estimate and correct for motion artifacts within, for example, image sequences and are often used in computer vision applications. A classical OF solution for the displacement between a fixed image f and a moving image g satisfies the following well-known equation:
      Δ    ⁢                  ⁢    r    =            Δ      ⁢                          ⁢              r        _              -                  ∇                  f          ⁡                      (            r            )                              ⁢                        [                                    g              ⁡                              (                                  r                  +                                      Δ                    ⁢                                                                                  ⁢                                          r                      _                                                                      )                                      -                          f              ⁡                              (                r                )                                              ]                                      λ            s                    +                                                                  ∇                                  f                  ⁡                                      (                    r                    )                                                                                      2                              where Δr is the total displacement between the images, and λs is a regularization parameter. Larger values of λs may allow for smoother solutions.
Conventional OF techniques assume that changes in image content are only due to motion. Thus, in conventional OF techniques, a 3D-velocity vector may describe pixel intensity values and the intensity values may be assumed to remain unchanged over small time intervals. However, correcting for artifacts related to local variations in image contrast, as might be encountered in comparing, for example, medical images taken with and without contrast agents, may not be amenable to conventional OF techniques employing classical solutions such as the above equation.